The noise performance of an analog-to-digital converter is determined in part by the noise performance of the analog modulator. In the case of a delta-sigma analog modulator, this noise can be of two types, the quantization noise and the thermal noise, which noise is a function of the architecture, filtering, etc., of the modulator. This is especially exhibited in the noise differences between multi-bit and single-bit modulators. Multi-bit delta-sigma modulators provide some advantages in quantization noise performance due their ability to increase resolution in the DAC portion of the modulator. The addition of an extra bit of resolution in the feedback DAC reduces quantization noise by 6 dB. Delta-sigma modulators are often designed to minimize quantization noise within some frequency band of interest. This minimization anticipates that a subsequent digital filter section will remove quantization noise outside the frequency band of interest.
The order of a delta-sigma modulator controls the amount of quantization noise that appears in a frequency band of interest. A modulator of order L will improve the signal-to-noise ratio by (6 L+3) dB for each doubling of the sampling frequency. For this reason, increasing modulator order has been recognized as a more efficient method of improving the dynamic range of a delta-sigma modulator than increasing the resolution of the DAC portion thereof.
One inherent disadvantage to a multi-bit delta-sigma modulator is the need to correct for non-idealities in a DAC having greater than two output levels. Correction for these non-idealities is discussed in Catalepe et. al., "Digitally Corrected Multi-Bit Sigma-Delta Data Converters", IEEE Proceedings ISCAS '89, May 1989 and Carley, "A Noise-Shaping Coder Topology for 15+Bit Converters", IEEE J. Solid-State Circuits, SC-24, April 1989.
The primary problems that are being addressed by researchers in the delta-sigma analog-to-digital converter field include the reduction of in-band quantization noise and the production of a stable modulator. For the most part, practical delta-sigma modulators often have relatively little quantization noise within their frequency band of interest, as their noise is dominated by thermal noise sources at the converter input, which normally comprises a switched-capacitor integrator. The noise limits of the switched-capacitor integrators are discussed in Hauser, M. W. and Brodersen, R. W., "Circuits and Technology Considerations for MOS Delta-Sigma A/D Converters", IEEE Proceedings ISCAS '86, May 1986, pp. 1310-1315.
In conventional delta-sigma converters having a bi-level output, the feedback DAC consists of a capacitor C.sub.1 and appropriate switches. The converter's optimal mean-square equivalent input noise current is given by: ##EQU1## Note that i.sup.2.sub.EQ increases linearly with the value of C.sub.1. Here f.sub.s is the modulator sampling frequency, f.sub.B is the bandwidth of interest, k is Boltzmann's constant, and T is the absolute temperature.
One type of multi-level delta-sigma modulator using a tri-level DAC is described in Paulos, "Improved Signal-to-Noise Ratio Using Tri-level Delta-Sigma Modulation", IEEE Proc. ISCAS '87, May 1987, pp. 436-466. In this type of structure, a "do nothing" state is provided such that a large percentage of sampling periods, no charge is delivered to the input node. The "do nothing" state results in lower quantization noise and provides some thermal noise advantages as well. The reason for this is that noise is only added to the modulator when C.sub.1 is switched. If the term .beta. denotes the probability of occurrence of the "do nothing" state, the equivalent input noise current is given by: EQU i.sub.EQ.sup.2 =(1-.beta.)4kTC.sub.1 f.sub.S f.sub.B ( 2)
It can be seen therefore that the tri-level system reduces the effective value of C.sub.1 some of the time (when compared to a bi-level system).
The kTC.sub.1 noise is the dominant thermal noise source in a properly designed delta-sigma converter. However, it should be understood that there are numerous other thermal noise sources that can impact the performance of high order delta-sigma modulators.
Once the loop filter parameters of the delta-sigma modulator are chosen, the values for the reference voltages on the quantizer in the tri-level system are selected to optimize in-band quantization noise. This provides a noise advantage but it does not directly address the thermal noise problems which tend to dominate the noise considerations in high order delta-sigma modulators. Therefore, there exists a need to address the thermal noise considerations of multi-level delta-sigma modulators utilizing multi-level DACs in the feedback path.